CAPÍTULO 3. GÉNEROS Y FORMATOS
3.1 Géneros informativos
3.2.1 Comedia de situación
(i) The effect of the inverse-square-root transformation on the error component of the multiplicative error model whose distribution is assumed to be
86
non-normal such as Gamma, Weibull, etc are suggested for investigations to establish if the results of this study will also be valid.
(ii) Since we only used simulations to establish that the Variance of the untransformed error component to that of the transformed is 4, we also suggest its establishment analytically.
87
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Table 3.1: COMPUTATION OF
92 0.010 0.99992502 0.00007500 0.155 0.94470721 0.05529300
0.015 0.99970031 0.00030000 0.160 0.94163225 0.05836800 0.020 0.99932659 0.00067300 0.165 0.93852446 0.06147600 0.025 0.99880501 0.00119500 0.170 0.93538739 0.06461300 0.030 0.99813720 0.00186300 0.175 0.93222440 0.06777600 0.035 0.99732519 0.00267500 0.180 0.92903869 0.07096100 0.040 0.99637147 0.00362900 0.185 0.92583333 0.07416700 0.045 0.99527886 0.00472100 0.190 0.92261120 0.07738900 0.050 0.99405059 0.00594900 0.195 0.91937505 0.08062500 0.055 0.99269018 0.00731000 0.200 0.91612748 0.08387300 0.060 0.99120149 0.00879900 0.205 0.91287093 0.08712900 0.065 0.98958860 0.01041100 0.210 0.90960772 0.09039200 0.070 0.98785584 0.01214400 0.215 0.90634001 0.09366000 0.075 0.98600775 0.01399200 0.220 0.90306986 0.09693000 0.080 0.98404899 0.01595100 0.225 0.89979918 0.10020100 0.085 0.98198438 0.01801600 0.230 0.89652976 0.10347000 0.090 0.97981881 0.02018100 0.235 0.89326328 0.10673700 0.095 0.97755725 0.02244300 0.240 0.89000132 0.10999900 0.100 0.97520469 0.02479500 0.245 0.88674534 0.11325500 0.105 0.97276613 0.02723400 0.250 0.88349669 0.11650300 0.110 0.97024653 0.02975300 0.255 0.88025665 0.11974300 0.115 0.96765082 0.03234900 0.260 0.87702640 0.12297400 0.120 0.96498387 0.03501600 0.265 0.87380702 0.12619300 0.125 0.96225045 0.03775000 0.270 0.87059952 0.12940000 0.130 0.95945523 0.04054500 0.275 0.86740484 0.13259500 0.135 0.95660279 0.04339700 0.280 0.86422383 0.13577600 0.140 0.95369754 0.04630200 0.285 0.86105729 0.13894300 0.145 0.95074378 0.04925600 0.290 0.85790594 0.14209400 0.150 0.94774567 0.05225400 0.295 0.85477043 0.14523000 0.300 0.85165139 0.14834900
Table 3.2: Conditions For Decimal places
3 2 1
93 Table 3.3: Simulation Results When = 0.06
X=etN
1,2
, 0.06 Y= t* 1t ,e et
e N
1,2
, 0.06Mean StD Variance Median AD p-value Mean StDev Variance Median
AD p-value
*
Var
Var t t
e e
1 0.06 0.0036 0.9927 .235 .788 1.0013 0.0303 0.000918 1.0037 .206 .867 4
1 0.06 0.0036 1.0009 .183 .908 1.0013 0.0302 0.000914 0.9995 .298 .580 4
1 0.06 0.0036 1.0002 .195 .889 1.0013 0.0303 0.000916 0.9999 .275 .654 4
1 0.06 0.0036 1.0029 .234 .790 1.0013 0.0303 0.000917 0.9985 .334 .505 4
1 0.06 0.0036 1.0037 .178 .918 1.0013 0.0302 0.000915 0.9982 .312 .546 4
1 0.06 0.0036 1.0045 .435 .294 1.0013 0.0301 0.000908 0.9978 .364 .433 4
1 0.06 0.0036 1.0037 .178 .918 1.0013 0.0302 0.000915 0.9982 .312 .546 4
1 0.06 0.0036 1.0013 .137 .976 1.0013 0.0302 0.00091 0.9993 .213 .851 4
1 0.06 0.0036 0.9941 .196 .888 1.0013 0.0302 0.000911 1.003 .302 .569 4
1 0.06 0.0036 1.0017 .250 .739 1.0014 0.0304 0.000924 0.9991 .453 .266 4
1 0.06 0.0036 1.0004 .200 .880 1.0013 0.0302 0.000915 0.9998 .314 .540 4
1 0.06 0.0036 1.0045 .435 .294 1.0013 0.0301 0.000908 0.9978 .364 .433 4
1 0.06 0.0036 0.9991 .183 .908 1.0013 0.0303 0.000916 1.0005 .214 .846 4
1 0.06 0.0036 0.9983 .250 .739 1.0013 0.0301 0.000908 1.0009 .206 .866 4
1 0.06 0.0036 1.001 .209 .859 1.0013 0.03 0.000901 0.9995 .241 .767 4
1 0.06 0.0036 1.0028 .195 .889 1.0013 0.0302 0.000913 0.9986 .284 .625 4
1 0.06 0.0036 1.0031 .141 .972 1.0013 0.0302 0.000911 0.9985 .208 .862 4
1 0.06 0.0036 0.9975 .310 .550 1.0013 0.0299 0.000894 1.0012 .232 .795 4
1 0.06 0.0036 1.0006 .262 .699 1.0014 0.0304 0.000924 0.9997 .385 .387 4
1 0.06 0.0036 0.9983 .182 .911 1.0013 0.0302 0.000913 1.0009 .318 .531 4
1 0.06 0.0036 0.9958 .150 .962 1.0013 0.0303 0.000916 1.0021 .218 .835 4
1 0.06 0.0036 0.9938 .290 .606 1.0013 0.0299 0.000896 1.0031 .185 .906 4
1 0.06 0.0036 0.9931 .450 .270 1.0013 0.03 0.000903 1.0035 .336 .503 4
1 0.06 0.0036 0.995 .199 .882 1.0013 0.0301 0.000907 1.0025 .390 .376 4
1 0.06 0.0036 0.9987 .216 .841 1.0013 0.0302 0.000914 1.0006 .315 .538 4
1 0.06 0.0036 0.9942 .311 .546 1.0013 0.03 0.000899 1.0029 .165 .940 4
NB i. 2 = (0.3752) = 0.00135 ii. 2.
94 Table 3.4: Simulation Results when = 0.1
X= etN
1,2 , 0.1 Y= t* 1t ,e et
e N
1,2 , 0.1Mean StD Variance Median AD p-value Mean StD Variance Median
AD p-value
*
Var Var
t t
e e
1 0.1 0.01 0.9878 .235 .788 1.0038 0.0514 0.00265 1.0061 .298 .582 4
1 0.1 0.01 1.0016 .183 .908 1.0038 0.0511 0.00262 0.9992 .457 .260 4
1 0.1 0.01 1.0003 .195 .889 1.0038 0.0513 0.00263 0.9998 .428 .306 4
1 0.1 0.01 1.0049 .234 .790 1.0038 0.0513 0.00264 0.9976 .502 .201 4
1 0.1 0.01 1.0062 .178 .918 1.0038 0.0512 0.00262 0.9969 .495 .211 4
1 0.1 0.01 1.0074 .435 .294 1.0038 0.0509 0.00259 0.9963 .424 313 4
1 0.1 0.01 1.0062 .178 .918 1.0038 0.0512 0.00262 0.9969 .495 .211 4
1 0.1 0.01 1.0022 .137 .976 1.0038 0.0509 0.00259 0.9989 .357 .450 4
1 0.1 0.01 0.9902 .196 .888 1.0038 0.051 0.0026 1.005 .464 .251 4
1 0.1 0.01 1.0029 .250 .739 1.0038 0.0516 0.00267 0.9986 .685 .071 4
1 0.1 0.01 1.0007 .200 .880 1.0038 0.0512 0.00262 0.9997 .495 .210 4
1 0.1 0.01 1.0074 .435 .294 1.0038 0.0509 0.00259 0.9963 .424 .313 4
1 0.1 0.01 0.9984 .183 .908 1.0038 0.0513 0.00263 1.0008 .326 .516 4
1 0.1 0.01 0.9971 .250 .739 1.0038 0.0509 0.00259 1.0014 .272 .664 4
1 0.1 0.01 1.0016 .209 .859 1.0037 0.0505 0.00255 0.9992 .359 .445 4
1 0.1 0.01 1.0047 .195 .889 1.0038 0.0511 0.00261 0.9977 .446 .277 4
1 0.1 0.01 1.0052 .141 .972 1.0038 0.051 0.0026 0.9974 346 .477 4
1 0.1 0.01 0.9959 .310 .550 1.0037 0.0502 0.00252 1.0021 .278 .642 4
1 0.1 0.01 1.0011 .262 .699 1.0038 0.0516 0.00266 0.9995 .554 .150 4
1 0.1 0.01 0.9971 .182 .911 1.0038 0.0511 0.00261 1.0014 .499 .205 4
1 0.1 0.01 0.9931 .150 .962 1.0038 0.0513 0.00263 1.0035 .368 .424 4
1 0.1 0.01 0.9897 .290 .606 1.0037 0.0503 0.00253 1.0052 .221 .827 4
1 0.1 0.01 0.9884 .450 .270 1.0037 0.0506 0.00256 1.0058 .366 .428 4
1 0.1 0.01 0.9917 .306 .559 1.0038 0.0508 0.00258 1.0042 .547 .156 4
1 0.1 0.01 0.9979 .199 .882 1.0038 0.0511 0.00261 1.0011 .497 .207 4
1 0.1 0.01 0.9904 .216 .841 1.0037 0.0504 0.00254 1.0048 .226 .815 4
NB i. 2 = 0.375 (.01) = 0.00375 ii. 2.
95 Table 3.5: Simulation Results when = 0.15
X= etN
1,2
, 0.15 Y= t* 1t ,t
e
e e N
1,2
, 0.15Mean StD Variance Median AD p-value Mean StDev Variance Median AD p-value
*
Var Var
t t
e e
1 0.15 0.0225 0.9818 .235 .788 1.0089 0.0803 0.00645 1.0092 .582 .126 3
1 0.15 0.0225 1.0024 .183 .908 1.0088 0.0791 0.00626 0.9988 .761 .046 4
1 0.15 0.0225 1.0005 .195 .889 1.0088 0.0798 0.00637 0.9997 .756 .047 4
1 0.15 0.0225 1.0073 .234 .790 1.0088 0.0798 0.00636 0.9964 .857 .027 4
1 0.15 0.0225 1.0093 .178 .918 1.0088 0.0792 0.00628 0.9954 .842 .029 4
1 0.15 0.0225 1.0111 .435 .294 1.0087 0.0788 0.0062 0.9945 .646 .089 4
1 0.15 0.0225 1.0093 .178 .918 1.0088 0.0792 0.00628 0.9954 .842 .029 4
1 0.15 0.0225 1.0034 .137 .976 1.0087 0.0786 0.00618 0.9983 .656 .085 4
1 0.15 0.0225 0.9853 .196 .888 1.0087 0.0788 0.00621 1.0075 .785 .040 3
1 0.15 0.0225 1.0043 .250 .739 1.0089 0.0804 0.00646 0.9979 1.109 .005 4
1 0.15 0.0225 1.001 .200 .880 1.0088 0.0793 0.00628 0.9995 .860 .026 4
1 0.15 0.0225 1.0111 .435 .294 1.0087 0.0788 0.0062 0.9945 .646 .089 4
1 0.15 0.0225 0.9976 .183 .908 1.0088 0.0796 0.00633 1.0012 .596 .119 4
1 0.15 0.0225 0.9957 .250 .739 1.0087 0.0788 0.00621 1.0022 .486 .221 4
1 0.15 0.0225 1.0025 .209 .859 1.0086 0.0775 0.00601 0.9988 .620 .104 4
1 0.15 0.0225 1.007 195 889 1.0088 0.0791 0.00626 0.9965 .779 .042 4
1 0.15 0.0225 1.0077 141 .972 1.0087 0.0787 0.00619 0.9962 .635 .095 4
1 0.15 0.0225 0.9938 .310 .550 1.0085 0.077 0.00593 1.0031 .450 .271 4
1 0.15 0.0225 1.0016 .262 .699 1.0089 0.0799 0.00639 0.9992 .880 .023 4
1 0.15 0.0225 0.9957 .182 .911 1.0087 0.0789 0.00622 1.0022 .838 .030 4
1 0.15 0.0225 0.9896 .500 .962 1.0088 0.0798 0.00636 1.0052 .701 .065 4
1 0.15 0.0225 0.9846 .290 .606 1.0085 0.077 0.00593 1.0078 .398 .361 4
1 0.15 0.0225 0.9826 .450 .270 1.0086 0.0781 0.00609 1.0088 .545 .157 4
1 0.15 0.0225 0.9876 .306 .559 1.0087 0.0782 0.00611 1.0063 .868 .025 4
1 0.15 0.0225 0.9968 .199 .882 1.0088 0.079 0.00624 1.0016 .860 .026 4
1 0.15 0.0225 0.9856 .216 .841 1.0085 0.0772 0.00596 1.0073 .419 .322 4
NB: (i) The p-value is less than 0.05 in 50% of the cases iii. 2 = (0.375) (0.0225) = 0.0084 (ii) The ratio of the two variances is less than 4 in 8% of the cases. iv. 2..
96 Table 3.6: Simulation Results when = 0.2
etN
1,2 , 0.2 *1
t ,
t t
e
e eN
1,2
, 0.2Mean StD Variance Median AD p-value Mean StDev Variance Median
AD
p-value
*
Var Var
t t
e e
1 0.2 0.04 0.9757 .235 .788 1.0167 0.1147 0.0132 1.0124 1.176 <0.005 3
1 0.2 0.04 1.0032 .183 .908 1.0162 0.1107 0.0123 0.9984 1.220 <0.005 3
1 0.2 0.04 1.0007 .195 .889 1.0165 0.1127 0.0127 0.9997 1.315 <0.005 3
1 0.2 0.04 1.0097 .234 .790 1.0164 0.1124 0.0126 0.9952 1.435 <0.005 3
1 0.2 0.04 1.0124 .178 .918 1.0163 0.1109 0.0123 0.9939 1.353 <0.005 3
1 0.2 0.04 1.0148 .435 .294 1.0161 0.1105 0.0122 0.9927 1.097 .007 3
1 0.2 0.04 1.0124 .178 .918 1.0163 0.1109 0.0123 0.9939 1.353 <0.005 3
1 0.2 0.04 1.0045 .137 .976 1.0161 0.1095 0.012 0.9978 1.117 .006 3
1 0.2 0.04 0.9803 .196 .888 1.0161 0.11 0.0121 1.01 1.276 <0.005 3
1 0.2 0.04 1.0057 .250 ..739 1.0166 0.1133 0.0128 0.9971 1.734 <0.005 3
1 0.2 0.04 1.0013 .200 .880 1.0163 0.111 0.0123 0.9994 1.418 <0.005 3
1 0.2 0.04 1.0149 .435 .294 1.0161 0.1105 0.0122 0.9927 1.097 .007 3
1 0.2 0.04 0.9968 .183 .908 1.0164 0.112 0.0125 1.0016 1.072 .008 3
1 0.2 0.04 0.9943 .250 .739 1.0162 0.1107 0.0123 1.0029 .915 0.019 3
1 0.2 0.04 1.0033 .209 .859 1.0157 0.1072 0.0115 0.9984 1.026 0.010 3
1 0.2 0.04 1.0094 .195 .889 1.0162 0.1109 0.0123 0.9953 1.293 <0.005 3
1 0.2 0.04 1.0103 .141 .972 1.0161 0.1097 0.012 0.9949 1.084 0.007 3
1 0.2 0.04 0.9917 .310 .550 1.0156 0.1066 0.0114 1.0042 .768 0.045 3
1 0.2 0.04 1.0021 .260 .699 1.0165 0.1119 0.0125 0.9989 1.371 <0.005 3
1 0.2 0.04 0.9942 .182 .911 1.0162 0.11 0.0121 1.0029 1.331 <0.005 3
1 0.2 0.04 0.9862 .150 .962 1.0165 0.1128 0.0127 1.007 1.267 <0.005 3
1 0.2 0.04 0.9795 .290 .606 1.0156 0.1064 0.0113 1.0104 .745 0.051 3
1 0.2 0.04 0.9768 .450 .270 1.0159 0.109 0.0119 1.0118 .933 .017 3
1 0.2 0.04 0.9835 .306 .559 1.0159 0.1084 0.0118 1.0084 1.348 <0.005 3
1 0.2 0.04 0.9958 .199 .882 1.0162 0.1101 0.0121 1.0021 1.402 <0.005 3
1 0.2 0.04 0.9808 .216 .841 1.0156 0.1066 0.0114 1.0097 .766 .045 3
NB: (i) The p-value is less than 0.05 in all the cases iii. 2 = 0.015 (ii) The ratio of the two variances is less than 4 in all the cases. iv.
* 1 3 2t 8
E e .
97
Table 3.7: Values of E(Y) and Var(Y) for [0.01,0.5]
2 e212 A B E(Y) Var(Y) Var(X) VarY/VarX 0.01 0.0001 0.0000000 1.00000 2.00000 1.00004 0.0000250 0.000100 4.00023 0.02 0.0004 0.0000000 1.00000 2.00000 1.00015 0.0001000 0.000400 4.00090 0.03 0.0009 0.0000000 1.00000 2.00000 1.00034 0.0002249 0.000900 4.00203 0.04 0.0016 0.0000000 1.00000 2.00000 1.00060 0.0003996 0.001600 4.00360 0.05 0.0025 0.0000000 1.00000 2.00000 1.00094 0.0006241 0.002500 4.00563 0.06 0.0036 0.0000000 1.00000 2.00000 1.00135 0.0008982 0.003600 4.00812 0.07 0.0049 0.0000000 1.00000 2.00000 1.00184 0.0012216 0.004900 4.01106 0.08 0.0064 0.0000000 1.00000 2.00000 1.00240 0.0015942 0.006400 4.01445 0.09 0.0081 0.0000000 1.00000 2.00000 1.00304 0.0020158 0.008100 4.01831 0.10 0.0100 0.0000000 1.00000 2.00000 1.00375 0.0024859 0.010000 4.02263 0.11 0.0121 0.0000000 1.00000 2.00000 1.00454 0.0030044 0.012100 4.02741 0.12 0.0144 0.0000000 1.00000 2.00000 1.00540 0.0035708 0.014400 4.03266 0.13 0.0169 0.0000000 1.00000 2.00000 1.00634 0.0041848 0.016900 4.03839 0.14 0.0196 0.0000000 1.00000 2.00000 1.00735 0.0048460 0.019600 4.04459 0.15 0.0225 0.0000000 1.00000 2.00000 1.00844 0.0055538 0.022500 4.05127 0.16 0.0256 0.0000000 1.00000 2.00000 1.00960 0.0063078 0.025600 4.05844 0.17 0.0289 0.0000000 1.00000 2.00000 1.01084 0.0071075 0.028900 4.06610 0.18 0.0324 0.0000002 1.00000 2.00000 1.01215 0.0079524 0.032400 4.07425 0.19 0.0361 0.0000010 1.00000 2.00000 1.01354 0.0088417 0.036100 4.08290 0.20 0.0400 0.0000037 1.00000 2.00000 1.01500 0.0097750 0.040000 4.09204 0.21 0.0441 0.0000119 1.00000 2.00000 1.01654 0.0107515 0.044099 4.10166 0.22 0.0484 0.0000326 1.00000 1.99999 1.01815 0.0117706 0.048397 4.11170 0.23 0.0529 0.0000785 0.99999 1.99999 1.01984 0.0128315 0.052893 4.12211 0.24 0.0576 0.0001699 0.99998 1.99997 1.02160 0.0139334 0.057584 4.13277 0.25 0.0625 0.0003355 0.99997 1.99994 1.02344 0.0150757 0.062467 4.14353 0.26 0.0676 0.0006134 0.99994 1.99988 1.02535 0.0162574 0.067536 4.15420 0.27 0.0729 0.0010503 0.99989 1.99979 1.02734 0.0174777 0.072787 4.16456 0.28 0.0784 0.0016993 0.99982 1.99964 1.02940 0.0187356 0.078210 4.17440 0.29 0.0841 0.0026181 0.99972 1.99944 1.03154 0.0200304 0.083797 4.18349 0.30 0.0900 0.0038659 0.99957 1.99914 1.03375 0.0213609 0.089537 4.19162 0.31 0.0961 0.005501 0.90769 1.99988 1.03604 0.0227263 0.095419 4.19861 0.32 0.1024 0.007576 0.91959 1.99979 1.03840 0.0241254 0.101431 4.20432 0.33 0.1089 0.010139 0.93148 1.99964 1.04084 0.0255573 0.107562 4.20865 0.34 0.1156 0.013230 0.94335 1.99944 1.04335 0.0270208 0.113799 4.21155 0.35 0.1225 0.016880 0.95521 1.99914 1.04594 0.0285147 0.120132 4.21299 0.36 0.1296 0.021110 0.96706 1.99874 1.04860 0.0300380 0.126551 4.21301 0.37 0.1369 0.025931 0.97889 1.99822 1.05134 0.0315895 0.133044 4.21167 0.38 0.1444 0.031348 0.99071 1.99756 1.05415 0.0331678 0.139605 4.20904 0.39 0.1521 0.037354 1.00252 1.99673 1.05704 0.0347717 0.146224 4.20525 0.40 0.1600 0.043937 1.01431 1.99573 1.06000 0.0364000 0.152895 4.20041 0.41 0.1681 0.051077 0.90769 1.99453 1.06304 0.0380513 0.159613 4.19467 0.42 0.1764 0.058750 0.91959 1.99312 1.06615 0.0397242 0.166372 4.18817
98
Table 3.7 Continues
0.43 0.1849 0.066926 0.95521 1.98758 1.06934 0.0414173 0.173168 4.18106 0.44 0.1936 0.075574 0.96706 1.98527 1.07260 0.0431292 0.179999 4.17349 0.45 0.2025 0.084658 0.97889 1.98273 1.07594 0.0448585 0.186862 4.16560 0.46 0.2116 0.094142 0.99071 1.97996 1.07935 0.0466036 0.193756 4.15753 0.47 0.2209 0.103989 1.00252 1.97696 1.08284 0.0483629 0.200678 4.14941 0.48 0.2304 0.114162 1.01431 1.99988 1.08640 0.0501350 0.207628 4.14138 0.49 0.2401 0.124623 0.90769 1.99979 1.09004 0.0519182 0.214607 4.13355 0.50 0.2500 0.135335 0.91959 1.99964 1.09375 0.0537109 0.221613 4.12603
99
Table 4.1: Time Series Decomposition Table for The Monthly Interest Rates Government Bond Yield 2-Year Securities, Reserve Bank of Australia. Jan 1976 – Dec 1993.
T Xt ˆ*
Mt ˆ*
St
e ˆ
*t Yt Mˆ*t ˆ*St
e ˆ
*t1 8.46 6.4945 1.00904 1.29096 0.343807 0.373735 0.99673 0.92294 2 8.50 6.6367 1.02472 1.24985 0.342997 0.371554 0.98857 0.93381 3 8.50 6.7776 1.02025 1.22925 0.342997 0.369394 0.99047 0.93747 4 8.47 6.9171 1.00158 1.22257 0.343604 0.367255 1.00016 0.93545 5 8.47 7.0552 1.00564 1.19379 0.343604 0.365138 0.99702 0.94384 6 8.47 7.1921 0.99741 1.18074 0.343604 0.363042 1.00214 0.94443 7 8.48 7.3276 0.99608 1.16183 0.343401 0.360968 1.00365 0.94787 8 8.48 7.4617 1.00873 1.12663 0.343401 0.358915 0.99498 0.96160 9 8.54 7.5945 0.99702 1.12786 0.342193 0.356883 1.00001 0.95883 10 8.56 7.7260 0.98500 1.12482 0.341793 0.354872 1.00637 0.95705 11 8.39 7.8561 0.98262 1.08685 0.345238 0.352883 1.00695 0.97158 12 8.89 7.9849 0.97193 1.14551 0.335389 0.350916 1.01299 0.94350 13 9.91 8.1123 1.00904 1.21065 0.317660 0.348969 0.99673 0.91327 14 9.89 8.2384 1.02472 1.17151 0.317982 0.347044 0.98857 0.92685 15 9.91 8.3632 1.02025 1.16144 0.317660 0.345140 0.99047 0.92923 16 9.91 8.4866 1.00158 1.16588 0.317660 0.343258 1.00016 0.92528 17 9.90 8.6087 1.00564 1.14355 0.317821 0.341397 0.99702 0.93373 18 9.88 8.7294 0.99741 1.13474 0.318142 0.339557 1.00214 0.93493 19 9.86 8.8488 0.99608 1.11866 0.318465 0.337739 1.00365 0.93950 20 9.86 8.9669 1.00873 1.09008 0.318465 0.335942 0.99498 0.95276 21 9.74 9.0836 0.99702 1.07547 0.320421 0.334167 1.00001 0.95886 22 9.42 9.1990 0.98500 1.03962 0.325818 0.332412 1.00637 0.97396 23 9.27 9.3130 0.98262 1.01298 0.328443 0.330680 1.00695 0.98638 24 9.26 9.4257 0.97193 1.01079 0.328620 0.328968 1.01299 0.98613 25 8.99 9.5371 1.00904 0.93419 0.333519 0.327278 0.99673 1.02242 26 8.83 9.6471 1.02472 0.89322 0.336527 0.325609 0.98857 1.04548 27 8.83 9.7558 1.02025 0.88714 0.336527 0.323962 0.99047 1.04878 28 8.83 9.8631 1.00158 0.89384 0.336527 0.322336 1.00016 1.04386 29 8.82 9.9691 1.00564 0.87977 0.336718 0.320731 0.99702 1.05299 30 8.83 10.0738 0.99741 0.87880 0.336527 0.319147 1.00214 1.05220 31 8.83 10.1771 0.99608 0.87105 0.336527 0.317585 1.00365 1.05579 32 8.79 10.2791 1.00873 0.84773 0.337292 0.316045 0.99498 1.07261 33 8.79 10.3797 0.99702 0.84937 0.337292 0.314525 1.00001 1.07237 34 8.69 10.4790 0.98500 0.84190 0.339227 0.313027 1.00637 1.07684 35 8.66 10.5770 0.98262 0.83324 0.339814 0.311551 1.00695 1.08319
100 Table 4.1 Continues
T Xt ˆ x
Mt ˆx
St eˆxt Yt ˆ y
Mt ˆy
St eˆty
36 8.67 10.6736 0.97193 0.83574 0.339618 0.310095 1.01299 1.08116 37 8.72 10.7689 1.00904 0.80248 0.338643 0.308661 0.99673 1.10074 38 8.77 10.8628 1.02472 0.78786 0.337676 0.307249 0.98857 1.11173 39 9.00 10.9554 1.02025 0.80521 0.333333 0.305858 0.99047 1.10032 40 9.61 11.0467 1.00158 0.86857 0.322581 0.304488 1.00016 1.05925 41 9.70 11.1366 1.00564 0.86612 0.321081 0.303139 0.99702 1.06235 42 9.94 11.2252 0.99741 0.88781 0.317181 0.301812 1.00214 1.04868 43 9.94 11.3124 0.99608 0.88214 0.317181 0.300506 1.00365 1.05165 44 9.94 11.3983 1.00873 0.86451 0.317181 0.299222 0.99498 1.06536 45 9.95 11.4829 0.99702 0.86910 0.317021 0.297959 1.00001 1.06397 46 9.94 11.5661 0.98500 0.87250 0.317181 0.296717 1.00637 1.06220 47 9.96 11.6479 0.98262 0.87021 0.316862 0.295497 1.00695 1.06490 48 9.97 11.7285 0.97193 0.87462 0.316703 0.294297 1.01299 1.06233 49 10.83 11.8077 1.00904 0.90898 0.303869 0.293120 0.99673 1.04007 50 10.75 11.8855 1.02472 0.88264 0.304997 0.291963 0.98857 1.05672 51 11.20 11.9620 1.02025 0.91772 0.298807 0.290828 0.99047 1.03732 52 11.40 12.0372 1.00158 0.94557 0.296174 0.289715 1.00016 1.02213 53 11.54 12.1111 1.00564 0.94750 0.294372 0.288622 0.99702 1.02297 54 11.50 12.1835 0.99741 0.94634 0.294884 0.287552 1.00214 1.02331 55 11.34 12.2547 0.99608 0.92900 0.296957 0.286502 1.00365 1.03272 56 11.50 12.3245 1.00873 0.92502 0.294884 0.285474 0.99498 1.03817 57 11.50 12.3930 0.99702 0.93072 0.294884 0.284467 1.00001 1.03661 58 11.58 12.4601 0.98500 0.94352 0.293864 0.283481 1.00637 1.03006 59 12.42 12.5259 0.98262 1.00908 0.283752 0.282517 1.00695 0.99744 60 12.85 12.5904 0.97193 1.05010 0.278964 0.281574 1.01299 0.97802 61 13.10 12.6535 1.00904 1.02601 0.276289 0.280653 0.99673 0.98769 62 13.12 12.7152 1.02472 1.00694 0.276079 0.279753 0.98857 0.99827 63 13.10 12.7757 1.02025 1.00504 0.276289 0.278874 0.99047 1.00026 64 13.15 12.8348 1.00158 1.02294 0.275764 0.278017 1.00016 0.99174 65 13.10 12.8925 1.00564 1.01039 0.276289 0.277180 0.99702 0.99977 66 13.20 12.9489 0.99741 1.02203 0.275241 0.276366 1.00214 0.99380 67 14.20 13.0040 0.99608 1.09627 0.265372 0.275572 1.00365 0.95948 68 14.75 13.0577 1.00873 1.11982 0.260378 0.274800 0.99498 0.95229 69 14.60 13.1101 0.99702 1.11697 0.261712 0.274050 1.00001 0.95497 70 14.60 13.1612 0.98500 1.12621 0.261712 0.273320 1.00637 0.95147 71 14.45 13.2109 0.98262 1.11314 0.263067 0.272613 1.00695 0.95833 72 14.50 13.2592 0.97193 1.12516 0.262613 0.271926 1.01299 0.95336 73 14.80 13.3063 1.00904 1.10229 0.259938 0.271261 0.99673 0.96140 74 15.85 13.3520 1.02472 1.15845 0.251180 0.270617 0.98857 0.93890 75 16.20 13.3963 1.02025 1.18529 0.248452 0.269994 0.99047 0.92906 76 16.50 13.4393 1.00158 1.22580 0.246183 0.269393 1.00016 0.91370 77 16.40 13.4810 1.00564 1.20970 0.246932 0.268813 0.99702 0.92135
101 Table 4.1 Continues
T Xt ˆ x
Mt ˆx
St eˆxt Yt ˆ y
Mt ˆy
St eˆty
78 16.40 13.5213 0.99741 1.21604 0.246932 0.268255 1.00214 0.91855 79 16.35 13.5603 0.99608 1.21047 0.247310 0.267718 1.00365 0.92041 80 16.10 13.5979 1.00873 1.17375 0.249222 0.267202 0.99498 0.93742 81 13.70 13.6342 0.99702 1.00783 0.270172 0.266708 1.00001 1.01298 82 13.50 13.6692 0.98500 1.00266 0.272166 0.266234 1.00637 1.01581 83 14.00 13.7028 0.98262 1.03976 0.267261 0.265783 1.00695 0.99862 84 12.30 13.7351 0.97193 0.92138 0.285133 0.265352 1.01299 1.06076 85 12.00 13.7661 1.00904 0.86389 0.288675 0.264943 0.99673 1.09315 86 14.35 13.7957 1.02472 1.01508 0.263982 0.264556 0.98857 1.00936 87 14.60 13.8239 1.02025 1.03518 0.261712 0.264189 0.99047 1.00015 88 12.50 13.8509 1.00158 0.90105 0.282843 0.263844 1.00016 1.07183 89 12.75 13.8765 1.00564 0.91367 0.280056 0.263521 0.99702 1.06593 90 13.70 13.9007 0.99741 0.98812 0.270172 0.263219 1.00214 1.02422 91 13.45 13.9236 0.99608 0.96979 0.272671 0.262938 1.00365 1.03324 92 13.55 13.9452 1.00873 0.96325 0.271663 0.262678 0.99498 1.03942 93 12.60 13.9654 0.99702 0.90493 0.281718 0.262440 1.00001 1.07345 94 12.00 13.9843 0.98500 0.87117 0.288675 0.262223 1.00637 1.09391 95 11.00 14.0018 0.98262 0.79951 0.301511 0.262028 1.00695 1.14274 96 11.60 14.0180 0.97193 0.85140 0.293610 0.261854 1.01299 1.10689 97 12.05 14.0329 1.00904 0.85100 0.288076 0.261701 0.99673 1.10440 98 12.35 14.0464 1.02472 0.85802 0.284555 0.261569 0.98857 1.10045 99 12.70 14.0586 1.02025 0.88544 0.280607 0.261459 0.99047 1.08356 100 12.45 14.0694 1.00158 0.88350 0.283410 0.261371 1.00016 1.08415 101 12.55 14.0789 1.00564 0.88640 0.282279 0.261303 0.99702 1.08350 102 12.20 14.0871 0.99741 0.86829 0.286299 0.261257 1.00214 1.09351 103 12.10 14.0939 0.99608 0.86191 0.287480 0.261233 1.00365 1.09647 104 11.15 14.0994 1.00873 0.78397 0.299476 0.261229 0.99498 1.15219 105 11.85 14.1035 0.99702 0.84273 0.290496 0.261247 1.00001 1.11195 106 12.10 14.1063 0.98500 0.87083 0.287480 0.261287 1.00637 1.09328 107 12.50 14.1078 0.98262 0.90171 0.282843 0.261347 1.00695 1.07478 108 12.90 14.1079 0.97193 0.94079 0.278423 0.261430 1.01299 1.05134 109 12.50 14.1067 1.00904 0.87816 0.282843 0.261533 0.99673 1.08503 110 13.20 14.1041 1.02472 0.91332 0.275241 0.261658 0.98857 1.06407 111 13.65 14.1002 1.02025 0.94886 0.270666 0.261804 0.99047 1.04380 112 13.65 14.0950 1.00158 0.96690 0.270666 0.261971 1.00016 1.03302 113 13.50 14.0884 1.00564 0.95286 0.272166 0.262160 0.99702 1.04127 114 13.45 14.0805 0.99741 0.95770 0.272671 0.262371 1.00214 1.03704 115 13.35 14.0712 0.99608 0.95248 0.273690 0.262602 1.00365 1.03843 116 14.45 14.0606 1.00873 1.01880 0.263067 0.262855 0.99498 1.00585 117 14.30 14.0487 0.99702 1.02093 0.264443 0.263129 1.00001 1.00498 118 15.05 14.0354 0.98500 1.08862 0.257770 0.263425 1.00637 0.97234 119 15.55 14.0208 0.98262 1.12868 0.253592 0.263742 1.00695 0.95488
102 Table 4.1 Continues
T Xt ˆ x
Mt ˆx
St eˆxt Yt ˆ y
Mt ˆy
St eˆty
120 15.65 14.0048 0.97193 1.14974 0.252780 0.264080 1.01299 0.94493 121 14.65 13.9875 1.00904 1.03798 0.261265 0.264440 0.99673 0.99124 122 14.15 13.9689 1.02472 0.98853 0.265841 0.264821 0.98857 1.01545 123 13.30 13.9489 1.02025 0.93456 0.274204 0.265223 0.99047 1.04381 124 12.65 13.9276 1.00158 0.90684 0.281161 0.265647 1.00016 1.05823 125 12.70 13.9049 1.00564 0.90822 0.280607 0.266092 0.99702 1.05770 126 12.80 13.8809 0.99741 0.92452 0.279508 0.266559 1.00214 1.04634 127 14.50 13.8555 0.99608 1.05063 0.262613 0.267047 1.00365 0.97982 128 15.10 13.8289 1.00873 1.08247 0.257343 0.267556 0.99498 0.96668 129 15.15 13.8008 0.99702 1.10104 0.256917 0.268086 1.00001 0.95833 130 14.30 13.7715 0.98500 1.05419 0.264443 0.268638 1.00637 0.97815 131 14.25 13.7408 0.98262 1.05540 0.264906 0.269211 1.00695 0.97722 132 14.05 13.7087 0.97193 1.05449 0.266785 0.269806 1.01299 0.97612 133 14.70 13.6753 1.00904 1.06529 0.260820 0.270422 0.99673 0.96766 134 15.05 13.6406 1.02472 1.07670 0.257770 0.271059 0.98857 0.96196 135 14.05 13.6045 1.02025 1.01225 0.266785 0.271718 0.99047 0.99129 136 13.80 13.5671 1.00158 1.01556 0.269191 0.272398 1.00016 0.98807 137 13.25 13.5284 1.00564 0.97393 0.274721 0.273099 0.99702 1.00895 138 13.00 13.4883 0.99741 0.96630 0.277350 0.273822 1.00214 1.01072 139 12.85 13.4469 0.99608 0.95937 0.278964 0.274566 1.00365 1.01232 140 12.60 13.4041 1.00873 0.93187 0.281718 0.275331 0.99498 1.02836 141 11.80 13.3600 0.99702 0.88587 0.291111 0.276118 1.00001 1.05429 142 13.00 13.3145 0.98500 0.99124 0.277350 0.276926 1.00637 0.99519 143 12.35 13.2678 0.98262 0.94729 0.284555 0.277755 1.00695 1.01741 144 11.45 13.2196 0.97193 0.89115 0.295527 0.278606 1.01299 1.04713 145 11.35 13.1702 1.00904 0.85407 0.296826 0.279478 0.99673 1.06556 146 11.55 13.1193 1.02472 0.85914 0.294245 0.280372 0.98857 1.06161 147 10.85 13.0672 1.02025 0.81385 0.303588 0.281287 0.99047 1.08967 148 10.90 13.0137 1.00158 0.83626 0.302891 0.282223 1.00016 1.07306 149 12.30 12.9589 1.00564 0.94383 0.285133 0.283180 0.99702 1.00991 150 11.70 12.9027 0.99741 0.90914 0.292353 0.284159 1.00214 1.02663 151 12.05 12.8452 0.99608 0.94179 0.288076 0.285160 1.00365 1.00655 152 12.30 12.7863 1.00873 0.95364 0.285133 0.286181 0.99498 1.00136 153 12.90 12.7261 0.99702 1.01669 0.278423 0.287224 1.00001 0.96935 154 13.05 12.6646 0.98500 1.04612 0.276818 0.288289 1.00637 0.95413 155 13.30 12.6017 0.98262 1.07408 0.274204 0.289374 1.00695 0.94104 156 13.85 12.5375 0.97193 1.13658 0.268705 0.290481 1.01299 0.91317 157 14.65 12.4720 1.00904 1.16410 0.261265 0.291610 0.99673 0.89888 158 15.05 12.4051 1.02472 1.18394 0.257770 0.292759 0.98857 0.89066 159 15.15 12.3369 1.02025 1.20366 0.256917 0.293930 0.99047 0.88248 160 14.85 12.2673 1.00158 1.20863 0.259500 0.295123 1.00016 0.87915 161 15.70 12.1964 1.00564 1.28005 0.252377 0.296337 0.99702 0.85420
103 Table 4.1 Continues
T Xt ˆ x
Mt ˆx
St eˆxt Yt ˆ y
Mt ˆy
St eˆty
162 15.40 12.1241 0.99741 1.27349 0.254824 0.297572 1.00214 0.85451 163 15.10 12.0505 0.99608 1.25799 0.257343 0.298828 1.00365 0.85804 164 14.80 11.9756 1.00873 1.22515 0.259938 0.300106 0.99498 0.87052 165 15.80 11.8993 0.99702 1.33178 0.251577 0.301405 1.00001 0.83467 166 15.80 11.8217 0.98500 1.35687 0.251577 0.302726 1.00637 0.82578 167 15.00 11.7427 0.98262 1.29998 0.258199 0.304068 1.00695 0.84329 168 14.40 11.6624 0.97193 1.27039 0.263523 0.305431 1.01299 0.85172 169 13.80 11.5808 1.00904 1.18095 0.269191 0.306816 0.99673 0.88025 170 14.30 11.4978 1.02472 1.21370 0.264443 0.308222 0.98857 0.86788 171 14.15 11.4135 1.02025 1.21516 0.265841 0.309649 0.99047 0.86678 172 14.45 11.3279 1.00158 1.27360 0.263067 0.311098 1.00016 0.84547 173 14.10 11.2409 1.00564 1.24731 0.266312 0.312568 0.99702 0.85456 174 14.05 11.1525 0.99741 1.26307 0.266785 0.314059 1.00214 0.84766 175 13.75 11.0629 0.99608 1.24779 0.269680 0.315572 1.00365 0.85147 176 13.30 10.9718 1.00873 1.20170 0.274204 0.317106 0.99498 0.86907 177 13.00 10.8795 0.99702 1.19848 0.277350 0.318661 1.00001 0.87035 178 12.55 10.7858 0.98500 1.18128 0.282279 0.320238 1.00637 0.87589 179 12.25 10.6907 0.98262 1.16612 0.285714 0.321836 1.00695 0.88164 180 11.85 10.5944 0.97193 1.15082 0.290496 0.323456 1.01299 0.88658 181 11.50 10.4967 1.00904 1.08577 0.294884 0.325097 0.99673 0.91004 182 11.10 10.3976 1.02472 1.04180 0.300150 0.326759 0.98857 0.92918 183 11.15 10.2972 1.02025 1.06133 0.299476 0.328442 0.99047 0.92058 184 10.70 10.1955 1.00158 1.04783 0.305709 0.330147 1.00016 0.92583 185 10.25 10.0924 1.00564 1.00992 0.312348 0.331873 0.99702 0.94398 186 10.55 9.9880 0.99741 1.05901 0.307875 0.333621 1.00214 0.92085 187 10.25 9.8822 0.99608 1.04130 0.312348 0.335390 1.00365 0.92791 188 10.30 9.7751 1.00873 1.04458 0.311588 0.337180 0.99498 0.92876 189 9.60 9.6667 0.99702 0.99607 0.322749 0.338992 1.00001 0.95208 190 8.40 9.5569 0.98500 0.89233 0.345033 0.340825 1.00637 1.00594 191 8.20 9.4458 0.98262 0.88347 0.349215 0.342679 1.00695 1.01204 192 7.25 9.3333 0.97193 0.79922 0.371391 0.344555 1.01299 1.06406 193 8.35 9.2195 1.00904 0.89757 0.346064 0.346452 0.99673 1.00216 194 8.25 9.1044 1.02472 0.88430 0.348155 0.348371 0.98857 1.01093 195 8.30 8.9879 1.02025 0.90514 0.347105 0.350310 0.99047 1.00038 196 7.40 8.8700 1.00158 0.83295 0.367607 0.352272 1.00016 1.04337 197 7.15 8.7509 1.00564 0.81248 0.373979 0.354254 0.99702 1.05884 198 6.35 8.6304 0.99741 0.73768 0.396838 0.356258 1.00214 1.11153 199 5.65 8.5085 0.99608 0.66665 0.420703 0.358283 1.00365 1.16995 200 7.40 8.3854 1.00873 0.87485 0.367607 0.360330 0.99498 1.02534 201 7.20 8.2608 0.99702 0.87419 0.372678 0.362398 1.00001 1.02836 202 7.05 8.1350 0.98500 0.87982 0.376622 0.364487 1.00637 1.02675 203 7.10 8.0078 0.98262 0.90232 0.375293 0.366597 1.00695 1.01666